Nonlinear ion-acoustic waves in a magnetized plasma and the Zakharov-Kuznetsov equation

We consider here the nonlinear development of ion-acoustic waves in a magnetized plasma, and give a further discussion of the analytical properties of the Zakharov-Kuznestov equation that governs the latter problem. First we discuss the solitary-wave solutions and show that they give a good description of recent experimental results about the manner in which the magnetic field influences the solitary waves. We then exhibit recurrence and Lagrange stability of solutions of the Zakharov-Kuznestov equation.